Survey data on expectations of a range of macroeconomic variables exhibit low-frequency drift. In a New Keynesian model consistent with these empirical properties, optimal policy in general delivers a positive inflation rate in the long run. Two special cases deliver classic outcomes under rational expectations: as the degree of low-frequency variation in beliefs goes to zero, the long-run inflation rate coincides with the inflation bias under optimal discretion; for non-zero low-frequency drift in beliefs, as households become highly patient valuing utility in any period equally, the optimal long-run inflation rate coincides with optimal commitment - price stability is optimal.